A model of judgment aggregation is presented in which judgments on propositions are not binary but come in degrees. The primitives are a set of propositions, an entailment relation, and a “triangular norm” which establishes a lower bound on the degree to which a proposition is true whenever it is entailed by a set of propositions. Under standard assumptions, we identify a necessary and sufficient condition for the collective judgments to be both deductively closed and free from veto power. This (...) condition says that the triangular norm used to establish the lower bound must contain a zero divisor. (shrink)

We investigate the social choice implications of what we call "the proximity condition". Loosely speaking, this condition says that whenever a profile moves "closer" to some individual's point of view, then the social choice cannot move "further away" from this individual's point of view. We apply this idea in two settings: merging functions and preference aggregation. The precise formulation of the proximity condition depends on the setting. First, restricting attention to merging functions that are interval scale invariant, we prove that (...) the only functions that satisfy proximity are dictatorships. Second, we prove that the only social welfare functions that satisfy proximity and a version of the Pareto criterion are dictatorships. We conclude that either proximity is not an attractive normative requirement after all, or we must give up some other social choice condition. Another possibility is that our normative intuition about proximity needs to be codified using different axioms. (shrink)

This paper is a survey of how economists and philosophers approach the issue of comparisons. More precisely, it is about what formal representation is appropriate whenever our ability to compare things breaks down. We restrict our attention to failures that arise with ordinal comparisons. We consider a number of formal approaches to this problem including one based on the idea of parity. We also consider the claim that the failure to compare things is a consequence of vagueness. We contrast two (...) theories of vagueness; fuzzy set theory and supervaluation theory. Some applications of these theories are described. (shrink)